This study investigates the effects of non-zero IMF B-y on the magnetotail B-y and fast earthward ion convection (V-perpendicular to > 200 km/s, "perpendicular to" indicates perpendicular to the magnetic field) in the near-lunar magnetotail plasma sheet using the plasma parameters and magnetic field detected by the ARTEMIS (Acceleration, Reconnection, Turbulence, and Electrodynamics of the Moon's Interaction with the Sun) P1 satellite during the period 2011-2022. We find that the magnetotail B-y with in the same direction as IMF B-y dominates the entire region. The IMF B-y influence is hemisphere-independent, but shows a dusk-dawn asymmetry with the IMF B-y effect being weaker in the premidnight region than in the postmidnight region. We also find that the IMF B-y influence on earthward fast convection results in an interhemispheric flow asymmetry and it is highly correlated with the direction of magnetotail B-y. The statistical results indicate that occasionally localized dynamics can have a significant effect on magnetotail B-y and V-perpendicular to.